Conair,
All I know about the JAA system is what I read here. There are apparently, rumours that Western Michigan University (where BA sends their cadets) have opened their doors to self improvers, albeit at great cost no doubt ;-)
I believe that there are no US schools approved for JAA Comm/ATPL training at the moment, other than the above mentioned and the Luthansa school in Arizona.
Again, rumours are the FAA and JAA are in talks to create an official conversion route for flight training, in a similar way to that of the maintainance side, i.e. FAR25 compliance.
However, with so much invested interest from European training organisations/airlines in the US, I'm sure eventually, some kind of agreement will be found.